Microalgal toxin(s): characteristics and importance

Prokaryotic and eukaryotic microalgae produce a wide array of compounds with biological activities. These include antibiotics, algicides, toxins, pharmaceutically active compounds and plant growth regulators. Toxic microalgae, in this sense, are common only among the cyanobacteria and dinoflagellates. The microalgal toxins is either important as material for useful drugs or one of the great mysteries in the world of biotoxicology. The aquatic poisons have long remained one of the great mysteries in the world of biotoxicology. There is evidence that these toxic organisms are on the increase, perhaps as a result of increased global pollution. The ability of cyanobacterial populations to produce potent toxins and annual examples of associated human and animal health problems have raised the position of cyanobacteria in the priorities for the management and protection of water quality in countries where health problems associated with the toxins have been perceived. The purpose of this review is to discuss the present understanding of microalgal toxins from microalgae in a manner that will stimulate interdisciplinary research with these microorganisms. Key Words: Toxin, cyanobacteria, microalgae, dinoflagellate. African Journal of Biotechnology Vol.3(12) 2004: 667-67

Transversality Conditions for Infinite Horizon Variational Problems on Time Scales

We consider problems of the calculus of variations on unbounded time scales. We prove the validity of the Euler-Lagrange equation on time scales for infinite horizon problems, and a new transversality condition.Comment: Submitted 6-October-2009; Accepted 19-March-2010 in revised form; for publication in "Optimization Letters"

The accumulation of heavy metals (Cd, Pb, Hg, Cr) and their state in phytoplanktonic algae and zooplanktonic organisms in Beysehir Lake and Mogan Lake, Turkey

Beysehir and Mogan Lakes are two shallow Lakes that are under environmental protection status. Phytoplanktonic dominant algae determined in Beysehir Lake were Oscillatoria sp., Cladophora sp.,Achnanthes sp., Gomphonema sp., Navicula sp., Cosmarium sp., Cymbella sp., Fragilaria sp., Oocystis sp., Spirogyra sp., Diatomae sp., Microcystis sp. and Staurastrum sp. While in Mogan Lake, Spirogyra sp., Zygnema sp., Euglena sp., Achnanthes sp., Cymbella sp., Fragilaria sp. Navicula sp., Scenedesmus sp., Oocystis sp., Synedra sp., Oscillatoria sp., Chlorella sp., Cosmarium sp. and Nitzshia sp. were determined. Zooplanktonic dominant organisms determined in Beysehir Lake were Eudiaptomus drieshi, Daphnia longispina and Brachionus calyciforus while Arctodiaptomus sp., Keratella quadrata, Filinia longiseta and Diaphanosoma lacustris were determined in Mogan Lake. Accumulation of heavy metals (Cd, Pb, Hg and Cr) in the water and plankton of Beysehir and Mogan Lakes was studiedseasonally, from April 2000 to December 2004. Higher concentration with all heavy metals was recorded in plankton. Mercury (Hg) was found in lowest and lead (Pb) in the highest correlation; however, the concentration of each metal varied seasonally. In addition, the seasonal changes inphytoplankton and zooplankton populations and species abundance were also determined. Some physical-chemical parameters of water and their correlation with heavy metals were also examined

Necessary Optimality Conditions for Higher-Order Infinite Horizon Variational Problems on Time Scales

We obtain Euler-Lagrange and transversality optimality conditions for higher-order infinite horizon variational problems on a time scale. The new necessary optimality conditions improve the classical results both in the continuous and discrete settings: our results seem new and interesting even in the particular cases when the time scale is the set of real numbers or the set of integers.Comment: This is a preprint of a paper whose final and definite form will appear in Journal of Optimization Theory and Applications (JOTA). Paper submitted 17-Nov-2011; revised 24-March-2012 and 10-April-2012; accepted for publication 15-April-201

Towards the Formalization of Fractional Calculus in Higher-Order Logic

Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to analyze a wide class of physical systems in various fields of science and engineering. In this paper, we describe an ongoing project which aims at formalizing the basic theories of fractional calculus in the HOL Light theorem prover. Mainly, we present the motivation and application of such formalization efforts, a roadmap to achieve our goals, current status of the project and future milestones.Comment: 9 page

Direct and Inverse Variational Problems on Time Scales: A Survey

We deal with direct and inverse problems of the calculus of variations on arbitrary time scales. Firstly, using the Euler-Lagrange equation and the strengthened Legendre condition, we give a general form for a variational functional to attain a local minimum at a given point of the vector space. Furthermore, we provide a necessary condition for a dynamic integro-differential equation to be an Euler-Lagrange equation (Helmholtz's problem of the calculus of variations on time scales). New and interesting results for the discrete and quantum settings are obtained as particular cases. Finally, we consider very general problems of the calculus of variations given by the composition of a certain scalar function with delta and nabla integrals of a vector valued field.Comment: This is a preprint of a paper whose final and definite form will be published in the Springer Volume 'Modeling, Dynamics, Optimization and Bioeconomics II', Edited by A. A. Pinto and D. Zilberman (Eds.), Springer Proceedings in Mathematics & Statistics. Submitted 03/Sept/2014; Accepted, after a revision, 19/Jan/201

Visibility graphs of fractional Wu-Baleanu time series

[EN] We study time series generated by the parametric family of fractional discrete maps introduced by Wu and Baleanu, presenting an alternative way of introducing these maps. For the values of the parameters that yield chaotic time series, we have studied the Shannon entropy of the degree distribution of the natural and horizontal visibility graphs associated to these series. In these cases, the degree distribution can be fitted with a power law. We have also compared the Shannon entropy and the exponent of the power law fitting for the different values of the fractionary exponent and the scaling factor of the model. Our results illustrate a connection between the fractionary exponent and the scaling factor of the maps, with the respect to the onset of the chaos.J.A. Conejero is supported Ministerio de Economia y Competitividad Grant Project MTM2016-75963-P. Carlos Lizama is supported by CONICYT, under Fondecyt Grant number 1180041. Cristobal Rodero-Gomez is funded by European Commission H2020 research and Innovation programme under the Marie Sklodowska-Curie grant agreement No. 764738.Conejero, JA.; Lizama, C.; Mira-Iglesias, A.; Rodero-Gómez, C. (2019). Visibility graphs of fractional Wu-Baleanu time series. The Journal of Difference Equations and Applications. 25(9-10):1321-1331. https://doi.org/10.1080/10236198.2019.1619714S13211331259-10Anand, K., & Bianconi, G. (2009). Entropy measures for networks: Toward an information theory of complex topologies. Physical Review E, 80(4). doi:10.1103/physreve.80.045102Barabási, A.-L., & Albert, R. (1999). Emergence of Scaling in Random Networks. Science, 286(5439), 509-512. doi:10.1126/science.286.5439.509Brzeziński, D. W. (2017). Comparison of Fractional Order Derivatives Computational Accuracy - Right Hand vs Left Hand Definition. Applied Mathematics and Nonlinear Sciences, 2(1), 237-248. doi:10.21042/amns.2017.1.00020Brzeziński, D. W. (2018). Review of numerical methods for NumILPT with computational accuracy assessment for fractional calculus. Applied Mathematics and Nonlinear Sciences, 3(2), 487-502. doi:10.2478/amns.2018.2.00038DONNER, R. V., SMALL, M., DONGES, J. F., MARWAN, N., ZOU, Y., XIANG, R., & KURTHS, J. (2011). RECURRENCE-BASED TIME SERIES ANALYSIS BY MEANS OF COMPLEX NETWORK METHODS. International Journal of Bifurcation and Chaos, 21(04), 1019-1046. doi:10.1142/s0218127411029021Edelman, M. (2015). On the fractional Eulerian numbers and equivalence of maps with long term power-law memory (integral Volterra equations of the second kind) to Grünvald-Letnikov fractional difference (differential) equations. Chaos: An Interdisciplinary Journal of Nonlinear Science, 25(7), 073103. doi:10.1063/1.4922834Edelman, M. (2018). On stability of fixed points and chaos in fractional systems. Chaos: An Interdisciplinary Journal of Nonlinear Science, 28(2), 023112. doi:10.1063/1.5016437Gao, Z.-K., Small, M., & Kurths, J. (2016). Complex network analysis of time series. EPL (Europhysics Letters), 116(5), 50001. doi:10.1209/0295-5075/116/50001Iacovacci, J., & Lacasa, L. (2016). Sequential visibility-graph motifs. Physical Review E, 93(4). doi:10.1103/physreve.93.042309Indahl, U. G., Naes, T., & Liland, K. H. (2018). A similarity index for comparing coupled matrices. Journal of Chemometrics, 32(10), e3049. doi:10.1002/cem.3049Kantz, H., & Schreiber, T. (2003). Nonlinear Time Series Analysis. doi:10.1017/cbo9780511755798Lacasa, L., & Iacovacci, J. (2017). Visibility graphs of random scalar fields and spatial data. Physical Review E, 96(1). doi:10.1103/physreve.96.012318Lacasa, L., Luque, B., Ballesteros, F., Luque, J., & Nuño, J. C. (2008). From time series to complex networks: The visibility graph. Proceedings of the National Academy of Sciences, 105(13), 4972-4975. doi:10.1073/pnas.0709247105Lizama, C. (2015). lp-maximal regularity for fractional difference equations on UMD spaces. Mathematische Nachrichten, 288(17-18), 2079-2092. doi:10.1002/mana.201400326Lizama, C. (2017). The Poisson distribution, abstract fractional difference equations, and stability. Proceedings of the American Mathematical Society, 145(9), 3809-3827. doi:10.1090/proc/12895Luque, B., Lacasa, L., Ballesteros, F., & Luque, J. (2009). Horizontal visibility graphs: Exact results for random time series. Physical Review E, 80(4). doi:10.1103/physreve.80.046103Luque, B., Lacasa, L., Ballesteros, F. J., & Robledo, A. (2011). Feigenbaum Graphs: A Complex Network Perspective of Chaos. PLoS ONE, 6(9), e22411. doi:10.1371/journal.pone.0022411Luque, B., Lacasa, L., & Robledo, A. (2012). Feigenbaum graphs at the onset of chaos. Physics Letters A, 376(47-48), 3625-3629. doi:10.1016/j.physleta.2012.10.050May, R. M. (1976). Simple mathematical models with very complicated dynamics. Nature, 261(5560), 459-467. doi:10.1038/261459a0Núñez, Á. M., Luque, B., Lacasa, L., Gómez, J. P., & Robledo, A. (2013). Horizontal visibility graphs generated by type-I intermittency. Physical Review E, 87(5). doi:10.1103/physreve.87.052801Ravetti, M. G., Carpi, L. C., Gonçalves, B. A., Frery, A. C., & Rosso, O. A. (2014). Distinguishing Noise from Chaos: Objective versus Subjective Criteria Using Horizontal Visibility Graph. PLoS ONE, 9(9), e108004. doi:10.1371/journal.pone.0108004Robledo, A. (2013). Generalized Statistical Mechanics at the Onset of Chaos. Entropy, 15(12), 5178-5222. doi:10.3390/e15125178Shannon, C. E. (1948). A Mathematical Theory of Communication. Bell System Technical Journal, 27(3), 379-423. doi:10.1002/j.1538-7305.1948.tb01338.xSong, C., Havlin, S., & Makse, H. A. (2006). Origins of fractality in the growth of complex networks. Nature Physics, 2(4), 275-281. doi:10.1038/nphys266West, J., Lacasa, L., Severini, S., & Teschendorff, A. (2012). Approximate entropy of network parameters. Physical Review E, 85(4). doi:10.1103/physreve.85.046111Wu, G.-C., & Baleanu, D. (2013). Discrete fractional logistic map and its chaos. Nonlinear Dynamics, 75(1-2), 283-287. doi:10.1007/s11071-013-1065-7Wu, G.-C., & Baleanu, D. (2014). Discrete chaos in fractional delayed logistic maps. Nonlinear Dynamics, 80(4), 1697-1703. doi:10.1007/s11071-014-1250-3Zhang, J., & Small, M. (2006). Complex Network from Pseudoperiodic Time Series: Topology versus Dynamics. Physical Review Letters, 96(23). doi:10.1103/physrevlett.96.23870

A novel lineage of the Capra genus discovered in the Taurus Mountains of Turkey using ancient genomics

Direkli Cave, located in the Taurus Mountains of southern Turkey, was occupied by Late Epipaleolithic hunters-gatherers for the seasonal hunting and processing of game including large numbers of wild goats. We report genomic data from new and published Capra specimens from Direkli Cave and, supplemented with historic genomes from multiple Capra species, find a novel lineage best represented by a ~14,000 year old 2.59 X genome sequenced from specimen Direkli4. This newly discovered Capra lineage is a sister clade to the Caucasian tur species (Capra cylindricornis and Capra caucasica), both now limited to the Caucasus region. We identify genomic regions introgressed in domestic goats with high affinity to Direkli4, and find that West Eurasian domestic goats in the past, but not those today, appear enriched for Direkli4-specific alleles at a genome-wide level. This forgotten 'Taurasian tur' likely survived Late Pleistocene climatic change in a Taurus Mountain refuge and its genomic fate is unknown